A multiple search operator heuristic for the max-k-cut problem

Fuda Ma () and Jin-Kao Hao ()
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Fuda Ma: Université d’Angers
Jin-Kao Hao: Université d’Angers

Annals of Operations Research, 2017, vol. 248, issue 1, No 15, 365-403

Abstract: Abstract The max-k-cut problem is to partition the vertices of an edge-weighted graph $$G = (V,E)$$ G = ( V , E ) into $$k\ge 2$$ k ≥ 2 disjoint subsets such that the weight sum of the edges crossing the different subsets is maximized. The problem is referred as the max-cut problem when $$k=2$$ k = 2 . In this work, we present a multiple operator heuristic (MOH) for the general max-k-cut problem. MOH employs five distinct search operators organized into three search phases to effectively explore the search space. Experiments on two sets of 91 well-known benchmark instances show that the proposed algorithm is highly effective on the max-k-cut problem and improves the current best known results (lower bounds) of most of the tested instances for $$k\in [3,5]$$ k ∈ [ 3 , 5 ] . For the popular special case $$k=2$$ k = 2 (i.e., the max-cut problem), MOH also performs remarkably well by discovering 4 improved best known results. We provide additional studies to shed light on the key ingredients of the algorithm.

Keywords: Max-k-cut and max-cut; Graph partition; Multiple search strategies; Tabu list; Heuristics (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10479-016-2234-0

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